Preheat oven to 375°F.
Heat 4 tablespoons butter, sugar and 1/4 cup cider in 10-inch ovenproof skillet over medium heat until butter is melted and mixture boils and thickens slightly, about 5 minutes. Remove skillet from heat.
Arrange apple quarters in skillet, cored sides up, in concentric circles, overlapping and wedging pieces together to fit. Heat to boiling over medium-high heat. Boil 15 to 20 minutes, depending on juiciness of apples, until sugar mixture becomes caramel colored. Remove from heat.
Meanwhile, place cake mix in large bowl. With pastry blender or two knives used scissors fashion, cut in remaining 6 tablespoons butter until mixture resembles coarse crumbs. Stir in remaining 1/2 cup apple cider, egg and walnuts until mixture is just moistened (batter will be thick). Spoon batter over apples in an even layer.
Bake in 375°F oven 35 to 40 minutes or until wooden pick inserted into cake (not apples) comes out clean and top is golden. Remove to wire rack to cool 10 minutes. Cover skillet tightly with inverted serving plate. Flip skillet and plate over. Carefully remove skillet. Let cake cool on platter 10 minutes.
Meanwhile, heat jam in small saucepan over medium heat until melted and smooth. Brush top of apples with jam. Serve warm or at room temperature.